Statistics Calculator
Paste any list of numbers and instantly get a full descriptive statistics summary including mean, median, mode, spread, and quartiles.
Example
For the data set 2, 4, 4, 4, 5, 5, 7, 9 (n = 8):
Sum = 40 Mean = 5
Median = 4.5 Mode = 4
Min/Max= 2 / 9 Range = 7
Variance (pop) = 4 SD (pop) = 2
SD (sample) = 2.138089935
Q1 = 4 Q3 = 6 IQR = 2
How it works
Type or paste numbers separated by commas, spaces, or new lines. The calculator parses every finite value and recomputes all statistics live.
Good to know
This Statistics Calculator turns a raw list of numbers into a complete descriptive-statistics summary in one step. Type or paste values separated by commas, spaces, or line breaks and it reports count, sum, mean, median, mode, min, max, range, population variance, both population and sample standard deviation, and the quartiles Q1, Q3, and IQR. It is built for students checking homework, teachers preparing examples, analysts doing a quick sanity check, and anyone who would otherwise reach for a spreadsheet just to find a mean and spread.
Reach for it whenever you have a small-to-medium data set and need the whole picture at once rather than computing each measure separately. Because everything recalculates live as you edit the box, it is handy for "what if" tweaks: drop an outlier, add a value, or paste a different column and watch every figure update instantly without pressing a button.
To read the output, start with the three centre measures. The mean is the arithmetic average, the median is the middle value (resistant to extreme numbers), and the mode is the most frequent value, shown as "none" when nothing repeats and as a comma-separated list when several values tie. For spread, use the range for a quick gap between smallest and largest, the IQR for the middle 50% of the data, and standard deviation for typical distance from the mean. A key detail: the tool gives both a population SD (dividing by n) and a sample SD (dividing by n-1), so pick the one that matches whether your numbers are the entire group or a sample of a larger one.
- Tip and caveat: results are rounded to six decimal places, the calculator silently ignores any non-numeric text you paste, sample SD and the quartiles show "n/a" when there are too few values, and the quartiles use the median-of-halves method, so they may differ slightly from Excel's QUARTILE function or a TI calculator that uses another quartile convention.
Frequently asked questions
What is the difference between population and sample standard deviation?
Population SD divides the sum of squared deviations by n, assuming your numbers are the entire group. Sample SD divides by n-1 (Bessel's correction), which better estimates the spread of a larger population from a sample. This tool shows both.
How are the quartiles Q1 and Q3 calculated?
It uses the median-of-halves method: sort the data, then take the median of the lower half for Q1 and the median of the upper half for Q3. When the count is odd, the overall median is excluded from both halves. IQR is simply Q3 minus Q1.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is the difference between variance and standard deviation?
Variance is the average of the squared distances of each value from the mean, so its units are squared. Standard deviation is the square root of the variance, which brings the figure back into the same units as your original data and makes it easier to interpret.
When should I use the median instead of the mean?
The median is often more representative when a data set is skewed or contains outliers, because extreme values pull the mean up or down but barely move the middle value. The mean is preferred for symmetric data and when you need a figure for further calculations like totals.
Can a data set have more than one mode?
Yes. A set with two most-frequent values is bimodal and one with several is multimodal; this calculator lists every value that ties for the highest frequency. If no value repeats, there is no mode and the tool shows "none".
What does the interquartile range (IQR) tell me?
The IQR is Q3 minus Q1 and measures the spread of the middle 50% of your sorted data. It is commonly used to gauge variability without being affected by extreme values and to flag outliers that fall well outside Q1 and Q3.
How many numbers do I need for these statistics to be meaningful?
Mean, median, and range can be computed from very few values, but sample standard deviation needs at least two numbers and quartiles need enough data to split into halves. Larger samples generally give more stable and trustworthy estimates of spread.
Why does my standard deviation differ from another calculator's result?
The most common reason is using population SD (dividing by n) versus sample SD (dividing by n-1). Make sure both tools are using the same one; this calculator shows both so you can match whichever your assignment or software expects.
Can I paste a column of numbers copied from a spreadsheet?
Yes. The input accepts values separated by commas, spaces, or new lines, so a copied spreadsheet column generally works directly. Any blank cells or non-numeric text are ignored during parsing.
Do mean, median, and mode always come out the same?
Only in a perfectly symmetric distribution. When data is skewed they separate, and comparing them is a quick way to judge skew: a mean noticeably above the median usually indicates a right-skewed set, and below it a left-skewed set.
Related calculators